Perhaps the most likely case of adding many numbers at once in a computer would be when trying to multiply more quickly by using many adders to add many numbers in a single clock cycle. Compared to the multiply algorithm in Chapter 3, a carry save scheme with many adders could multiply more than 10 times faster. Th is exercise estimates the cost and speed of a combinational multiplier to multiply two positive 16-bit numbers. Assume that you have 16 intermediate terms M15, M14, …, M0, called partial products, that contain the multiplicand ANDed with multiplier bits m15, m14, …, m0. Th e idea is to use carry save adders to reduce the n operands into 2n/3 in parallel groups of three, and do this repeatedly until you get two large numbers to add together with a traditional adder. 

First, show the block organization of the 16-bit carry save adders to add these 16 terms, as shown on the right in Figure B.14.1. Then calculate the delays to add these 16 numbers. Compare this time to the iterative multiplication scheme in Chapter 3 but only assume 16 iterations using a 16-bit adder that has full carry lookahead whose speed was calculated in Exercise B.29.

Figure B.14.1